C(7,2)*(.9)^5*(.1)^2, or about .124 = 12.4%
For the desired outcome, considering the seven patients, you
need:
(Survive,Survive,Survive,Survive,Survive,Die,Die)
(Survive,Survive,Survive,Survive,Die,Survive,Die)
(Survive,Survive,Survive,Die,Survive,Survive,Die)
.
.
.
(Die,Die,Survive,Survive,Survive,Survive,Survive)
There are C(7,2) [the number of combinations of 7 things taken 2
at a time] = 21 possible desired outcomes. The probability of each
of these outcomes is (.9)*(.9)*(.9)*(.9)*(.9)*(.1)*(.1).
Multiplying 21 by (.9)*(.9)*(.9)*(.9)*(.9)*(.1)*(.1) yields the
answer.